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Vorticity Direction and Regularity of Solutions to the Navier-Stokes Equations

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Hugo Beirão da Veiga

    (Università di Pisa, Dipartimento di Matematica)

  • Yoshikazu Giga

    (University of Tokyo, Graduate School of Mathematical Sciences)

  • Zoran Grujić

    (University of Virginia, Department of Mathematics)

Abstract

It has been well documented – both in computational simulations of the 3D Navier-Stokes equations and the experiments with 3D incompressible turbulent fluid flows – that the regions of intense vorticity self-organize in coherent vortex structures, most notably, vortex filaments. One of the morphological characteristics of these structures is local coherence of the vorticity direction. The goal of this chapter is to review several avenues taken by the mathematical fluids community in order to study how the local coherence of the vorticity direction – a purely geometric condition – influences the possible formation of singularities in solutions to the 3D Navier-Stokes equations.

Suggested Citation

  • Hugo Beirão da Veiga & Yoshikazu Giga & Zoran Grujić, 2018. "Vorticity Direction and Regularity of Solutions to the Navier-Stokes Equations," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 18, pages 901-932, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_18
    DOI: 10.1007/978-3-319-13344-7_18
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